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MATH2001 final exam information

创建日期：2024-04-26 10:20:32

所属分类：数学mathematics

标签： MATH2001

Vector calculus

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MATH2001/MATH7000

final exam information
Final examination: 12 questions (10 marks per question), 10 minutes
“reading” time + 2 hours + 15 minutes admin/upload time, open book. I
will post the cover sheet on Blackboard once it has been finalised.
Know the trigonometric identities
cos2(θ) + sin2(θ) = 1, cos2(θ) =
1
2
+
1
2
cos(2θ).
Not examinable
• Workbook Sections 3.4-3.5 (almost exact ODEs and integrating fac-
tors);
• Workbook Section 4.3 (the catenary problem);
• You will not be asked to reproduce the inductive proof in Workbook
Section 15.4, but you should know the result;
• Workbook Section 16.5.1 (systems of differential equations);
• Workbook Section 19.4 (quadric surfaces);
• You will not be asked to prove the theorems of Green, Gauss or Stokes.
1
Examinable
• ODEs
– Various methods of solving first order ODEs, especially exact equa-
tions;
– Existence and uniqueness criteria, examples of method of successive
approximations
– Second order linear nonhomogeneous ODEs: Wronskian, Abel’s Theo-
rem, variation of parameters, method of undetermined coefficients;
– Hyperbolic functions: definitions, identities, inverse functions.
• Linear algebra
– Vector spaces, inner product spaces, properties of an inner product,
transition matrices, linear independence, span, basis;
– Gaussian elimination, row echelon form, solving systems of linear equa-
tions, rank;
– Orthogonality in inner product spaces, orthogonal complement, or-
thogonal projection onto a subspace, orthonormal basis, Gram-Schmidt
process;
– Least squares approximation in an inner product space;
– Orthogonal matrices, transition matrices between orthonormal bases;
– Complex matrices - unitary, hermitian, normal - related results;
– Eigenvalues/eigenvectors: diagonalisation, diagonalisation by orthogo-
nal/unitary matrices, quadratic forms, conic sections;
– Using diagonalisation to classify critical points of a function on n-
dimensions.
2
• Double & triple integrals
– Double integrals in rectangular and polar coordinates, Jacobian;
– General variable transformations in double integrals, Jacobian, image.
– Triple integrals in rectangular, cylindrical and spherical coordinates,
Jacobian;
– Determine bounds, evaluation;
– Changing the order of integration in an iterated integral;
– Applications of multiple integrals such as area and volume, calculating
mass, locating centre of mass, moments of inertia;
– You should understand the formulae for the mass, centre of mass and
moments of inertia;
• Vector calculus
– Flux of a vector field across a curve in 2D or surface in 3D, divergence,
flux integrals, Gauss’ divergence theorem;
– Parameterisation of curves and surfaces, surface integrals, surface area;
– Line integrals in 2D, 3D, curl, conservative vector fields, potential func-
tions, Green’s theorem, Stokes’ theorem;
– Make sure you know the theorems of Green, Gauss and Stokes, and
under what conditions they can be applied.

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关键词一关键词二关键词三关键词四关键词五和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 EMESTER1 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